The Laws of Motion of a Cylinder, &'c. 287 
be equal between themfelves, provided the effects 
of the friction of the column, and the furrounding 
matter increafe directly as the fpace penetrated: On 
the other hand, if the values of g thus found be 
unequal, it is evident, that the retarding force, occa- 
fioned by the caufe laft mentioned, varies in a ratio 
different from that affumed in the hypothefis. 
Should any one think of trying this experiment, in 
order to throw fome light on the nature of the re- 
tarding force arifing from this kind of impact, it will 
be proper to ufe a cylinder or right-angled paralle- 
lopiped, confifting of a hard polifhed fubfance, and 
containing fome kind of heavy matter, fuch as lead, 
in order to fix the center of gravity of the whole, 
neareft the furface on which the impact is intended 
tobe made. ‘The inftrument being thus prepared, 
fhould be dropt from different heights on a bed of © 
fand, which has been previgufly moiftened, to give it 
tenacity, and comprefled by a force fo applied as to 
make its denfity uniform, or nearly fo. ‘This man- 
ner of managing the experiment, not only fimpli- 
fies the operation, but renders the expreffion for g 
lefs complex; for, fince the weight of the falling 
block is the fame with that of the fyftem, o and 6 
are equal; and as the impact is firft made on the fur- 
face of the Obftacle, p and P vanifh out of the equa- 
+ 4bx ab X 
Pee ew 
ter all it is highly probable, that the variable part of, 
tne retarding force obferves a ratio which is com- 
pounded 
; b 
tion: confequently g = 
